{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn\n",
    "\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "seaborn.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 连续型分布"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 均匀分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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   "source": [
    "from scipy.stats import uniform\n",
    "\n",
    "x = np.linspace(-1, 3.5, 1000)  # -1到3.5区间内生成1000个点\n",
    "\n",
    "# 均匀分布\n",
    "uniform_rv_0 = uniform()  \n",
    "uniform_rv_1 = uniform(loc=0.5, scale=2)\n",
    "\n",
    "plt.plot(x, uniform_rv_0.pdf(x), color='r', lw=5, alpha=0.6, label='[0,1]')\n",
    "plt.plot(x, uniform_rv_1.pdf(x), color='b', lw=5, alpha=0.6, label='[0.5,2.5]')\n",
    "plt.legend(loc='best', frameon=False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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   "source": [
    "x = np.linspace(0, 3.5, 1000)\n",
    "\n",
    "uniform_rv = uniform(1, 2)\n",
    "uniform_rvs = uniform_rv.rvs(100000)  # 随机抽样100000个点\n",
    "\n",
    "plt.plot(x, uniform_rv.pdf(x), 'r-', lw=5, alpha=0.6, label='[1,3]')\n",
    "plt.hist(uniform_rvs, color='b', density=True, alpha=0.6, bins=50, edgecolor='k')\n",
    "plt.legend(loc='best', frameon=False)\n",
    "\n",
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 正态分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
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     "metadata": {},
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   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "\n",
    "# 构造正态分布函数\n",
    "norm_0 = norm(loc=0, scale=1)\n",
    "norm_1 = norm(loc=1, scale=2)\n",
    "\n",
    "x = np.linspace(-10, 10, 1000)\n",
    "ax.plot(x, norm_0.pdf(x), color='red', lw=5, alpha=0.6, label='loc=0, scale=1')\n",
    "ax.plot(x, norm_1.pdf(x), color='blue', lw=5, alpha=0.6, label='loc=1, scale=2')\n",
    "ax.legend(loc='best', frameon=False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
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   "source": [
    "norm_rv = norm(loc=0, scale=1)\n",
    "norm_rvs = norm_rv.rvs(size=100000)  # 抽样\n",
    "x = np.linspace(-10, 10, 1000)\n",
    "\n",
    "plt.plot(x, norm_rv.pdf(x), 'r', lw=5, alpha=0.6, label=\"`$\\\\mu$=0,$\\\\sigma=1$`\")\n",
    "plt.hist(norm_rvs, density=True, bins=50, alpha=0.6, edgecolor='k')\n",
    "plt.legend()\n",
    "plt.show()"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 指数分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
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     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "from scipy.stats import expon\n",
    "\n",
    "x = np.linspace(0, 10, 1000)\n",
    "expon_rv_0 = expon()  # 默认scale=1\n",
    "expon_rv_1 = expon(scale=2)\n",
    "\n",
    "plt.plot(x, expon_rv_0.pdf(x), color='r', lw=5, alpha=0.6, label='`$\\\\lambda$`=1')\n",
    "plt.plot(x, expon_rv_1.pdf(x), color='b', lw=5, alpha=0.6, label='`$\\\\lambda$`=0.5')\n",
    "plt.legend(loc='best', frameon=False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
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   "source": [
    "x = np.linspace(0, 10, 1000)\n",
    "expon_rv = expon()\n",
    "expon_rvs = expon_rv.rvs(100000)\n",
    "\n",
    "plt.plot(x, expon_rv.pdf(x), color='r', lw=5, alpha=0.6, label='`$\\\\lambda$`=1')\n",
    "plt.hist(expon_rvs, color='b', density=True, alpha=0.6, bins=50, edgecolor='k')\n",
    "plt.legend(loc='best', frameon=False)\n",
    "\n",
    "plt.show()"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 离散型分布"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 二项分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
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       "  </clipPath>\n",
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       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "\n",
    "fig, ax = plt.subplots(3, 1)\n",
    "params = [(10, 0.25), (10, 0.5), (10, 0.8)]\n",
    "x = range(0, 11)\n",
    "\n",
    "for i in range(len(params)):\n",
    "    binom_rv = binom(n=params[i][0], p=params[i][1])\n",
    "    ax[i].set_title('n={},p={}'.format(params[i][0], params[i][1]))\n",
    "    ax[i].plot(x, binom_rv.pmf(x), 'bo', ms=8)\n",
    "    ax[i].vlines(x, 0, binom_rv.pmf(x), colors='b', lw=3)\n",
    "    ax[i].set_xlim(0, 10)\n",
    "    ax[i].set_ylim(0, 0.35)\n",
    "    ax[i].set_xticks(x)\n",
    "    ax[i].set_yticks([0, 0.1, 0.2, 0.3])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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